One way of thinking about this, as noted in an article from Coding Wheel, is to look at the ratio of even and odd numbers starting from one. What you'll discover is that no matter what number you stop at, there will never be more even numbers than odd numbers in that sequence. The coin flips work in much the same way.

Prof Diaconis first realised that coin flips were not random after he and his colleagues managed to rig a coin-flipping machine to get a coin to land heads every time.

He and his team then asked human subjects do the same thing over and over, recording the results with a high-speed camera. Though the results were a little more random, they still ended up with the 51-49 per cent margin.

Prof Diaconis noted that the randomness is attributed to the fact that when humans flip coins, there are a number of different motions the coin is likely to make.

For instance, he showed how coins don't just move end to end, but also in a circular motion, like a tossed pizza.

He also found that there are ways to flip a coin where it looks like it is tumbling in the air, but in reality, it doesn't move at all.

Prof Diaconis proved this by tying a ribbon to a coin and showing how in four out of 10 times the ribbon would remain flat after the coin was caught.

While the margin is relatively small, it's enough to maybe get you reconsidering using a coin toss to settle your next argument.

In another startling discovery, Prof Diaconis determined that the probability of guessing which side comes up of a spinning copper-plated penny is also skewed more in one direction.

According to Prof Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time.

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Comments on this story

MB of Aus Posted at 11:21 AM December 04, 2012

Without having read this paper, I can see the one issue. It seems the foundation of the argument is that the side the coin starts on adds to the probability of that side being the outcome. The problem with this scenario is that it only holds true if that is a possible outcome. If someone were to 'flip' a coin and it not even go through half a rotation from heads to tails for example, I think it would be fair to say the person 'calling' would reject that it was a legitimate flip.
Unless a person were to develop a particularly repeatable action (like the machine) then the large number of random inputs results in 50% either way. Valid arguement could be constructed if it could be proven that during its rotation it spends more time of the rotation on one side than the other - but would need to take into account if the coin is caught or left to fall, and on to what surface

Davin Posted at 11:13 AM December 04, 2012

An Aussie $2 coin lands on heads 100% of the time!

Apples of Sydney Posted at 8:27 AM December 04, 2012

Even if this was true, if the person calling heads/tails doesn't know the way the coin is positioned in the flippers hand, they have a 50/50 chance of guessing correctly. Also the more flips a coin does, the less effect the one extra up facing has on the result.
They really should have analysed whether the weighting of the head or tails side had an effect as that is the only difference between the two options (though obviously different per type of coin) and it is the only thing that the caller knows as he doesn't know what side is pointing up to start with.

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